Enzyme Inhibition Calculator Formula

Understand the math behind the enzyme inhibition calculator. Each variable explained with a worked example.

Formulas Used

Apparent Km (Competitive)

km_app_comp = km * alpha

Velocity (Competitive Inhibition)

v_competitive = vmax * substrate / (km * alpha + substrate)

Velocity (Noncompetitive Inhibition)

v_noncompetitive = vmax / alpha * substrate / (km + substrate)

Variables

VariableDescriptionDefault
vmaxVmax (uninhibited)(umol/min)100
kmKm (uninhibited)(uM)50
inhibitorInhibitor Concentration [I](uM)20
kiInhibition Constant (Ki)(uM)10
substrateSubstrate Concentration [S](uM)50
alphaDerived value= 1 + inhibitor / kicalculated

How It Works

Enzyme Inhibition Types

Competitive Inhibition

Inhibitor binds to the active site, increasing apparent Km while Vmax remains unchanged.

v = Vmax × [S] / (alpha × Km + [S]), where alpha = 1 + [I]/Ki

Noncompetitive Inhibition

Inhibitor binds away from the active site, decreasing apparent Vmax while Km remains unchanged.

v = (Vmax/alpha) × [S] / (Km + [S])

Competitive inhibition can be overcome by high substrate concentration; noncompetitive cannot.

Worked Example

Vmax=100, Km=50 uM, [I]=20 uM, Ki=10 uM, [S]=50 uM.

vmax = 100km = 50inhibitor = 20ki = 10substrate = 50
  1. 01alpha = 1 + 20/10 = 3.0
  2. 02Competitive: v = 100 × 50 / (50 × 3 + 50) = 5000 / 200 = 25.0 umol/min
  3. 03Noncompetitive: v = (100/3) × 50 / (50 + 50) = 33.33 × 0.5 = 16.67 umol/min

Frequently Asked Questions

How do I distinguish competitive from noncompetitive?

On a Lineweaver-Burk plot: competitive inhibition changes the slope but not the y-intercept (lines converge on y-axis). Noncompetitive changes the y-intercept but not the x-intercept (lines converge on x-axis).

What is uncompetitive inhibition?

Uncompetitive inhibitors bind only to the enzyme-substrate complex, decreasing both apparent Vmax and Km by the same factor. On LB plots, this gives parallel lines.

How is Ki determined experimentally?

Measure kinetics at several inhibitor concentrations. Plot apparent Km (competitive) or apparent 1/Vmax (noncompetitive) vs [I]. The x-intercept of this secondary plot gives -Ki.

Ready to run the numbers?

Open Enzyme Inhibition Calculator